IKMC 2022 - Grades 7-8 - Self-study

Question 1

Meike paddled around five buoys, as shown. Around which buoys did she paddle in a clockwise direction?

1. 2, 3, 4
2. 1, 2, 3
3. 1, 3, 5
4. 2, 4, 5
5. 2, 3, 5

Question 2

Question 3

Kengu jumps on the number line. Starting at 0, he always makes two large jumps followed by three small jumps, as shown, and repeats this routine. On which number will he land?

1. 82
2. 83
3. 84
4. 85
5. 86

Question 4

Question 5

Rob has a brick whose shortest side is 4 cm. He uses several identical bricks to build the cube shown. What are the dimensions, in cm, of one brick?

1. $4\times6\times12$
2. $4\times6\times16$
3. $4\times8\times12$
4. $4\times8\times16$
5. $4\times12\times16$

Question 6

The black-and-white caterpillar shown curls up to sleep. Which picture could be seen?

Question 7

There are five empty spaces in the statement shown. Sania fills four with plus signs and one with a minus sign so that the statement is correct. Where should she put the minus sign?

1. Between 6 and 9
2. Between 9 and 12
3. Between 12 and 15
4. Between 15 and 18
5. Between 18 and 21

Question 8

There are five big trees and three paths in a park. In which region should a new tree be planted so that, for each path, there are equally many trees on its two sides?

1. A
2. B
3. C
4. D
5. E

Question 9

1. 25
2. 50
3. 75
4. 100
5. 150

Question 10

Gerard wrote a sum of the squares of two numbers, as shown. Some digits are covered by ink. What is the last digit of the first number?

1. 3
2. 4
3. 5
4. 6
5. 7

Question 11

The distance between two shelves in Monica’s cupboard is 36 cm. A stack of 8 identical glasses is 42 cm tall, and a stack of 2 is 18 cm tall. What is the greatest number of glasses that can be stacked and still fit?

1. 3
2. 4
3. 5
4. 6
5. 7

Question 12

On a standard die, opposite faces have a total of 7 dots. Four standard dice are glued together in a straight row as shown. What is the minimum number of dots on the whole exposed surface?

1. 52
2. 54
3. 56
4. 58
5. 60

Question 13

1. 10
2. 11
3. 12
4. 14
5. 16

Question 14

Tony planted tulips and daisies in a square flowerbed of side 12 m, arranged as shown. What is the total area of the regions planted with daisies?

1. $48\,\mathrm{m}^2$
2. $46\,\mathrm{m}^2$
3. $44\,\mathrm{m}^2$
4. $40\,\mathrm{m}^2$
5. $36\,\mathrm{m}^2$

Question 15

1. 23:00
2. 19:40
3. 15:40
4. 14:00
5. 11:20

Question 16

1. 7
2. 8
3. 9
4. 10
5. 11

Question 17

Place the numbers 1 to 8, once each, in the eight circles shown. Each number by an arrow is the product of the three numbers on that straight line. What is the sum of the numbers in the three bottom circles?

1. 11
2. 12
3. 15
4. 17
5. 19

Question 18

The intersection of a circle and a triangle has area 45% of their union. The part of the triangle outside the circle has area 40% of their union. What percentage of the circle lies outside the triangle?

1. 20%
2. 25%
3. 30%
4. 35%
5. 50%

Question 19

In how many ways can the shape on the left be completely covered by nine tiles like those on the right? Tiles may have the three orientations shown, with no gaps or overlaps.

1. 1
2. 6
3. 8
4. 9
5. 12

Question 20

1. $\frac16$
2. $\frac15$
3. $\frac14$
4. $\frac13$
5. $\frac12$